%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : REL033-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 07:41:25 AM UTC 2025
% Result : Unsatisfiable 234.84s 235.25s
% Output : CNFRefutation 234.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of clauses : 349 ( 349 unt; 0 nHn; 42 RR)
% Number of literals : 349 ( 348 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 602 ( 63 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
composition(meet(sk1,sk2),sk3) != meet(sk1,composition(sk2,sk3)),
file('theBenchmark.p',goals_15) ).
cnf(c1,axiom,
composition(X,one) = X,
file('REL001-0.ax',composition_identity_6) ).
cnf(c2,axiom,
converse(converse(X)) = X,
file('REL001-0.ax',converse_idempotence_8) ).
cnf(c3,axiom,
composition(sk1,top) = sk1,
file('theBenchmark.p',goals_14) ).
cnf(c4,axiom,
join(X,Y) = join(Y,X),
file('REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(c5,axiom,
top = join(X,complement(X)),
file('REL001-0.ax',def_top_12) ).
cnf(c6,plain,
join(X,complement(X)) = top,
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
zero = meet(X,complement(X)),
file('REL001-0.ax',def_zero_13) ).
cnf(c8,plain,
meet(X,complement(X)) = zero,
inference(equational,[status(thm)],[c7]) ).
cnf(c9,axiom,
converse(join(X,Y)) = join(converse(X),converse(Y)),
file('REL001-0.ax',converse_additivity_9) ).
cnf(c10,plain,
join(converse(X),converse(Y)) = converse(join(X,Y)),
inference(equational,[status(thm)],[c9]) ).
cnf(c11,axiom,
converse(composition(X,Y)) = composition(converse(Y),converse(X)),
file('REL001-0.ax',converse_multiplicativity_10) ).
cnf(c12,plain,
composition(converse(X),converse(Y)) = converse(composition(Y,X)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,axiom,
join(X,join(Y,Z)) = join(join(X,Y),Z),
file('REL001-0.ax',maddux2_join_associativity_2) ).
cnf(c14,plain,
join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
composition(X,composition(Y,Z)) = composition(composition(X,Y),Z),
file('REL001-0.ax',composition_associativity_5) ).
cnf(c16,plain,
composition(composition(X,Y),Z) = composition(X,composition(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,plain,
composition(X,composition(one,Y)) = composition(X,Y),
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c18,plain,
composition(sk1,composition(top,X)) = composition(sk1,X),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c19,plain,
converse(composition(converse(X),Y)) = composition(converse(Y),X),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c20,plain,
composition(converse(one),X) = X,
inference(equational,[status(thm)],[c1,c2,c19]) ).
cnf(c21,plain,
converse(one) = one,
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c22,plain,
composition(one,X) = X,
inference(equational,[status(thm)],[c17,c20]) ).
cnf(c23,plain,
converse(composition(X,converse(Y))) = composition(Y,converse(X)),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c24,plain,
converse(join(converse(X),Y)) = join(X,converse(Y)),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c25,plain,
converse(join(X,converse(Y))) = join(converse(X),Y),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c26,plain,
join(X,join(Y,Z)) = join(Y,join(X,Z)),
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c27,axiom,
meet(X,Y) = complement(join(complement(X),complement(Y))),
file('REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(c28,plain,
complement(join(complement(X),complement(Y))) = meet(X,Y),
inference(equational,[status(thm)],[c27]) ).
cnf(c29,plain,
complement(top) = zero,
inference(equational,[status(thm)],[c6,c8,c28]) ).
cnf(c30,plain,
meet(X,Y) = meet(Y,X),
inference(equational,[status(thm)],[c4,c28]) ).
cnf(c31,plain,
join(zero,top) = top,
inference(equational,[status(thm)],[c4,c6,c29]) ).
cnf(c33,plain,
complement(join(zero,complement(X))) = meet(top,X),
inference(equational,[status(thm)],[c28,c29]) ).
cnf(c35,plain,
join(X,join(complement(X),Y)) = join(top,Y),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c36,plain,
join(top,complement(complement(X))) = join(X,top),
inference(equational,[status(thm)],[c6,c35]) ).
cnf(c38,plain,
join(zero,join(top,X)) = join(top,X),
inference(equational,[status(thm)],[c26,c29,c35]) ).
cnf(c39,plain,
join(one,converse(X)) = converse(join(one,X)),
inference(equational,[status(thm)],[c10,c21]) ).
cnf(c40,plain,
join(zero,join(X,top)) = join(top,X),
inference(equational,[status(thm)],[c4,c38]) ).
cnf(c41,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(equational,[status(thm)],[c6,c24]) ).
cnf(c42,plain,
join(zero,converse(top)) = converse(top),
inference(equational,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
join(top,converse(zero)) = top,
inference(equational,[status(thm)],[c2,c4,c25,c42]) ).
cnf(c44,plain,
join(X,join(Y,complement(X))) = join(Y,top),
inference(equational,[status(thm)],[c6,c26]) ).
cnf(c46,axiom,
composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
file('REL001-0.ax',composition_distributivity_7) ).
cnf(c47,plain,
join(composition(X,Y),composition(Z,Y)) = composition(join(X,Z),Y),
inference(equational,[status(thm)],[c46]) ).
cnf(c48,plain,
join(sk1,composition(X,top)) = composition(join(sk1,X),top),
inference(equational,[status(thm)],[c3,c47]) ).
cnf(c49,plain,
composition(join(sk1,sk1),top) = join(sk1,sk1),
inference(equational,[status(thm)],[c3,c48]) ).
cnf(c50,plain,
composition(join(one,sk1),top) = join(top,sk1),
inference(equational,[status(thm)],[c4,c20,c21,c48]) ).
cnf(c51,plain,
join(X,composition(Y,X)) = composition(join(one,Y),X),
inference(equational,[status(thm)],[c20,c21,c47]) ).
cnf(c52,plain,
converse(join(one,one)) = join(one,one),
inference(equational,[status(thm)],[c21,c39]) ).
cnf(c54,plain,
join(X,join(Y,complement(join(X,Y)))) = top,
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c56,plain,
join(converse(X),join(converse(Y),Z)) = join(converse(join(X,Y)),Z),
inference(equational,[status(thm)],[c10,c14]) ).
cnf(c58,plain,
composition(converse(X),composition(converse(Y),Z)) = composition(converse(composition(Y,X)),Z),
inference(equational,[status(thm)],[c12,c16]) ).
cnf(c60,plain,
complement(join(complement(X),meet(Y,Z))) = meet(X,join(complement(Y),complement(Z))),
inference(equational,[status(thm)],[c28]) ).
cnf(c61,plain,
complement(join(meet(X,Y),complement(Z))) = meet(join(complement(X),complement(Y)),Z),
inference(equational,[status(thm)],[c28]) ).
cnf(c62,plain,
join(X,join(Y,complement(join(Y,X)))) = top,
inference(equational,[status(thm)],[c26,c54]) ).
cnf(c66,plain,
converse(join(X,join(converse(Y),Z))) = join(Y,converse(join(X,Z))),
inference(equational,[status(thm)],[c24,c26]) ).
cnf(c67,plain,
join(converse(X),join(Y,converse(Z))) = join(converse(join(X,Z)),Y),
inference(equational,[status(thm)],[c4,c56]) ).
cnf(c75,plain,
join(complement(X),join(complement(Y),meet(X,Y))) = top,
inference(equational,[status(thm)],[c6,c14,c28]) ).
cnf(c76,plain,
join(zero,join(complement(X),meet(X,top))) = top,
inference(equational,[status(thm)],[c26,c29,c75]) ).
cnf(c77,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(equational,[status(thm)],[c29,c76]) ).
cnf(c79,plain,
meet(meet(X,Y),join(complement(X),complement(Y))) = zero,
inference(equational,[status(thm)],[c8,c28,c30]) ).
cnf(c83,plain,
meet(top,join(complement(X),complement(Y))) = complement(join(zero,meet(X,Y))),
inference(equational,[status(thm)],[c29,c60]) ).
cnf(c86,plain,
join(composition(converse(X),Y),converse(Z)) = converse(join(composition(converse(Y),X),Z)),
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c89,plain,
join(converse(X),composition(Y,converse(Z))) = converse(join(X,composition(Z,converse(Y)))),
inference(equational,[status(thm)],[c10,c23]) ).
cnf(c90,plain,
composition(join(converse(X),Y),converse(Z)) = converse(composition(Z,join(X,converse(Y)))),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c91,plain,
composition(join(X,converse(Y)),converse(Z)) = converse(composition(Z,join(converse(X),Y))),
inference(equational,[status(thm)],[c12,c24]) ).
cnf(c93,plain,
composition(converse(X),join(Y,converse(Z))) = converse(composition(join(converse(Y),Z),X)),
inference(equational,[status(thm)],[c12,c24]) ).
cnf(c96,plain,
converse(join(X,composition(X,Y))) = converse(composition(X,join(one,Y))),
inference(equational,[status(thm)],[c10,c12,c39,c51]) ).
cnf(c97,plain,
join(X,composition(X,Y)) = composition(X,join(one,Y)),
inference(equational,[status(thm)],[c2,c96]) ).
cnf(c98,plain,
composition(sk1,join(one,top)) = join(sk1,sk1),
inference(equational,[status(thm)],[c48,c49,c97]) ).
cnf(c99,plain,
composition(join(one,X),X) = composition(X,join(one,X)),
inference(equational,[status(thm)],[c51,c97]) ).
cnf(c104,plain,
join(converse(join(one,X)),Y) = join(one,join(Y,converse(X))),
inference(equational,[status(thm)],[c21,c67]) ).
cnf(c108,plain,
join(top,join(complement(X),meet(Y,X))) = join(Y,top),
inference(equational,[status(thm)],[c35,c75]) ).
cnf(c109,plain,
join(top,meet(X,top)) = join(X,top),
inference(equational,[status(thm)],[c35,c108]) ).
cnf(c117,plain,
join(zero,join(X,join(top,Y))) = join(X,join(top,Y)),
inference(equational,[status(thm)],[c26,c38]) ).
cnf(c125,plain,
join(complement(converse(X)),converse(join(Y,X))) = join(top,converse(Y)),
inference(equational,[status(thm)],[c4,c6,c56]) ).
cnf(c126,plain,
join(complement(X),join(Y,X)) = join(top,Y),
inference(equational,[status(thm)],[c2,c10,c125]) ).
cnf(c130,plain,
join(X,converse(join(complement(converse(X)),Y))) = converse(join(top,Y)),
inference(equational,[status(thm)],[c24,c35]) ).
cnf(c134,plain,
composition(join(sk1,sk1),composition(top,X)) = composition(join(sk1,sk1),X),
inference(equational,[status(thm)],[c16,c49]) ).
cnf(c136,plain,
meet(meet(X,Y),join(complement(Y),complement(X))) = zero,
inference(equational,[status(thm)],[c30,c79]) ).
cnf(c139,axiom,
join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
file('REL001-0.ax',converse_cancellativity_11) ).
cnf(c140,plain,
join(complement(X),composition(converse(Y),complement(composition(Y,X)))) = complement(X),
inference(equational,[status(thm)],[c4,c139]) ).
cnf(c141,plain,
join(complement(X),complement(X)) = complement(X),
inference(equational,[status(thm)],[c20,c22,c140]) ).
cnf(c142,plain,
join(zero,zero) = zero,
inference(equational,[status(thm)],[c29,c141]) ).
cnf(c143,plain,
complement(complement(X)) = meet(X,X),
inference(equational,[status(thm)],[c28,c141]) ).
cnf(c144,plain,
meet(top,top) = complement(zero),
inference(equational,[status(thm)],[c29,c143]) ).
cnf(c145,plain,
join(top,complement(X)) = top,
inference(equational,[status(thm)],[c4,c6,c44,c141]) ).
cnf(c146,plain,
join(X,top) = top,
inference(equational,[status(thm)],[c36,c145]) ).
cnf(c147,plain,
join(top,X) = top,
inference(equational,[status(thm)],[c40,c117,c145,c146]) ).
cnf(c148,plain,
converse(top) = top,
inference(equational,[status(thm)],[c130,c147]) ).
cnf(c149,plain,
join(sk1,sk1) = sk1,
inference(equational,[status(thm)],[c3,c98,c146]) ).
cnf(c150,plain,
join(zero,composition(converse(sk1),complement(sk1))) = zero,
inference(equational,[status(thm)],[c3,c29,c140]) ).
cnf(c152,plain,
join(zero,join(X,zero)) = join(X,zero),
inference(equational,[status(thm)],[c26,c142]) ).
cnf(c153,plain,
join(zero,join(zero,X)) = join(zero,X),
inference(equational,[status(thm)],[c14,c142]) ).
cnf(c154,plain,
composition(join(one,X),top) = top,
inference(equational,[status(thm)],[c51,c147]) ).
cnf(c155,plain,
composition(top,top) = top,
inference(equational,[status(thm)],[c99,c146,c154]) ).
cnf(c156,plain,
composition(top,zero) = zero,
inference(equational,[status(thm)],[c29,c51,c140,c146,c148,c155]) ).
cnf(c157,plain,
composition(top,join(one,X)) = top,
inference(equational,[status(thm)],[c97,c147]) ).
cnf(c159,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(one),
inference(equational,[status(thm)],[c1,c140]) ).
cnf(c166,plain,
composition(converse(X),top) = converse(composition(top,X)),
inference(equational,[status(thm)],[c93,c146,c148]) ).
cnf(c167,plain,
composition(top,converse(X)) = converse(composition(X,top)),
inference(equational,[status(thm)],[c91,c146,c148]) ).
cnf(c169,plain,
composition(sk1,join(one,X)) = sk1,
inference(equational,[status(thm)],[c3,c18,c157]) ).
cnf(c173,plain,
join(complement(one),composition(X,complement(converse(X)))) = complement(one),
inference(equational,[status(thm)],[c2,c159]) ).
cnf(c178,plain,
join(complement(X),join(Y,complement(X))) = join(Y,complement(X)),
inference(equational,[status(thm)],[c26,c141]) ).
cnf(c189,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(equational,[status(thm)],[c29,c140]) ).
cnf(c195,plain,
join(X,converse(join(Y,complement(converse(X))))) = top,
inference(equational,[status(thm)],[c4,c10,c41,c67,c146,c148]) ).
cnf(c203,plain,
composition(join(one,X),zero) = zero,
inference(equational,[status(thm)],[c4,c47,c51,c146,c156]) ).
cnf(c207,plain,
composition(join(one,sk1),composition(top,X)) = composition(top,X),
inference(equational,[status(thm)],[c18,c47,c51,c147]) ).
cnf(c211,plain,
join(composition(X,Y),join(composition(Z,Y),W)) = join(composition(join(X,Z),Y),W),
inference(equational,[status(thm)],[c14,c47]) ).
cnf(c212,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(one,Y),X),Z),
inference(equational,[status(thm)],[c20,c21,c211]) ).
cnf(c213,plain,
join(X,join(composition(Y,X),Z)) = join(composition(join(Y,one),X),Z),
inference(equational,[status(thm)],[c20,c21,c26,c211]) ).
cnf(c219,plain,
join(X,join(X,Y)) = join(composition(join(one,one),X),Y),
inference(equational,[status(thm)],[c22,c212]) ).
cnf(c223,plain,
join(X,join(Y,composition(Z,X))) = join(composition(join(one,Z),X),Y),
inference(equational,[status(thm)],[c4,c212]) ).
cnf(c224,plain,
join(X,composition(join(one,Y),Z)) = join(Z,join(X,composition(Y,Z))),
inference(equational,[status(thm)],[c26,c51]) ).
cnf(c225,plain,
join(X,composition(Y,composition(Z,X))) = composition(join(one,composition(Y,Z)),X),
inference(equational,[status(thm)],[c16,c51]) ).
cnf(c226,plain,
join(X,join(composition(Y,X),Z)) = join(Z,composition(join(one,Y),X)),
inference(equational,[status(thm)],[c4,c212]) ).
cnf(c232,plain,
join(complement(X),composition(Y,complement(composition(converse(Y),X)))) = complement(X),
inference(equational,[status(thm)],[c2,c140]) ).
cnf(c233,plain,
join(zero,composition(X,complement(converse(composition(top,X))))) = zero,
inference(equational,[status(thm)],[c29,c166,c232]) ).
cnf(c236,plain,
join(zero,complement(composition(converse(sk1),complement(sk1)))) = top,
inference(equational,[status(thm)],[c4,c126,c147,c150]) ).
cnf(c237,plain,
meet(top,composition(converse(sk1),complement(sk1))) = zero,
inference(equational,[status(thm)],[c29,c33,c236]) ).
cnf(c238,plain,
composition(converse(join(one,join(one,sk1))),zero) = zero,
inference(equational,[status(thm)],[c29,c39,c50,c51,c147,c189]) ).
cnf(c239,plain,
join(zero,join(composition(X,zero),Y)) = join(zero,Y),
inference(equational,[status(thm)],[c104,c203,c211,c238]) ).
cnf(c247,plain,
converse(join(composition(X,Y),composition(X,converse(Z)))) = converse(composition(X,join(Y,converse(Z)))),
inference(equational,[status(thm)],[c12,c47,c89,c90]) ).
cnf(c248,plain,
composition(join(one,X),converse(sk1)) = converse(sk1),
inference(equational,[status(thm)],[c3,c23,c39,c97,c147,c247]) ).
cnf(c251,plain,
composition(X,converse(join(Y,Y))) = composition(join(X,X),converse(Y)),
inference(equational,[status(thm)],[c10,c23,c47,c247]) ).
cnf(c252,plain,
composition(join(X,X),Y) = composition(X,join(Y,Y)),
inference(equational,[status(thm)],[c2,c10,c251]) ).
cnf(c255,plain,
composition(top,join(X,X)) = composition(top,X),
inference(equational,[status(thm)],[c147,c207,c252]) ).
cnf(c257,plain,
converse(composition(X,join(Y,Y))) = converse(composition(join(X,X),Y)),
inference(equational,[status(thm)],[c10,c12,c251]) ).
cnf(c258,plain,
composition(join(X,X),complement(Y)) = composition(X,complement(Y)),
inference(equational,[status(thm)],[c141,c252]) ).
cnf(c259,plain,
composition(complement(X),join(Y,Y)) = composition(complement(X),Y),
inference(equational,[status(thm)],[c141,c252]) ).
cnf(c263,plain,
composition(converse(X),join(Y,Y)) = composition(converse(join(X,X)),Y),
inference(equational,[status(thm)],[c10,c19,c257]) ).
cnf(c269,plain,
composition(join(X,join(one,Y)),converse(sk1)) = converse(sk1),
inference(equational,[status(thm)],[c26,c248]) ).
cnf(c270,plain,
converse(join(composition(X,Y),composition(X,Z))) = converse(composition(X,join(Y,Z))),
inference(equational,[status(thm)],[c2,c247]) ).
cnf(c271,plain,
join(composition(X,Y),composition(X,Z)) = composition(X,join(Y,Z)),
inference(equational,[status(thm)],[c2,c270]) ).
cnf(c278,plain,
composition(sk1,join(composition(top,X),Y)) = composition(sk1,join(X,Y)),
inference(equational,[status(thm)],[c134,c149,c271]) ).
cnf(c280,plain,
composition(sk1,converse(join(X,join(one,Y)))) = sk1,
inference(equational,[status(thm)],[c2,c23,c269]) ).
cnf(c288,plain,
composition(join(one,X),composition(converse(sk1),Y)) = composition(converse(sk1),Y),
inference(equational,[status(thm)],[c16,c248]) ).
cnf(c290,plain,
composition(top,composition(converse(sk1),X)) = composition(converse(sk1),X),
inference(equational,[status(thm)],[c195,c288]) ).
cnf(c293,plain,
composition(join(X,X),meet(Y,Z)) = composition(X,meet(Y,Z)),
inference(equational,[status(thm)],[c28,c258]) ).
cnf(c299,plain,
composition(meet(X,Y),join(Z,Z)) = composition(meet(X,Y),Z),
inference(equational,[status(thm)],[c28,c259]) ).
cnf(c317,plain,
composition(zero,join(one,complement(converse(zero)))) = zero,
inference(equational,[status(thm)],[c97,c156,c233]) ).
cnf(c321,plain,
join(complement(composition(X,Y)),composition(join(Z,X),Y)) = top,
inference(equational,[status(thm)],[c4,c6,c146,c211]) ).
cnf(c322,plain,
join(converse(sk1),complement(composition(X,converse(sk1)))) = top,
inference(equational,[status(thm)],[c4,c248,c321]) ).
cnf(c324,plain,
join(sk1,converse(complement(composition(X,converse(sk1))))) = top,
inference(equational,[status(thm)],[c24,c148,c322]) ).
cnf(c340,plain,
composition(join(one,one),converse(X)) = converse(composition(X,join(one,one))),
inference(equational,[status(thm)],[c23,c52]) ).
cnf(c353,plain,
composition(sk1,join(X,complement(composition(top,X)))) = sk1,
inference(equational,[status(thm)],[c3,c6,c278]) ).
cnf(c359,plain,
join(zero,join(X,composition(Y,zero))) = join(X,zero),
inference(equational,[status(thm)],[c152,c153,c203,c224]) ).
cnf(c378,plain,
join(converse(zero),complement(composition(converse(complement(sk1)),sk1))) = top,
inference(equational,[status(thm)],[c4,c19,c43,c125,c150]) ).
cnf(c382,plain,
join(sk1,converse(complement(converse(composition(sk1,X))))) = top,
inference(equational,[status(thm)],[c10,c12,c149,c263,c324]) ).
cnf(c384,plain,
converse(join(composition(X,join(Y,Y)),Z)) = converse(join(composition(join(X,X),Y),Z)),
inference(equational,[status(thm)],[c2,c10,c12,c86,c251]) ).
cnf(c400,plain,
join(composition(X,Y),join(Z,composition(W,Y))) = join(composition(join(W,X),Y),Z),
inference(equational,[status(thm)],[c4,c14,c211]) ).
cnf(c414,plain,
join(X,join(composition(complement(one),X),Y)) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c6,c212]) ).
cnf(c415,plain,
join(X,join(composition(top,X),Y)) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c14,c255,c259,c414]) ).
cnf(c434,plain,
composition(converse(composition(top,X)),Y) = composition(converse(X),composition(top,Y)),
inference(equational,[status(thm)],[c58,c148]) ).
cnf(c435,plain,
join(X,join(Y,join(complement(join(X,Y)),Z))) = top,
inference(equational,[status(thm)],[c14,c54,c147]) ).
cnf(c440,plain,
join(X,join(Y,composition(top,X))) = join(composition(top,X),Y),
inference(equational,[status(thm)],[c146,c223]) ).
cnf(c443,plain,
join(X,composition(top,join(X,Y))) = composition(top,join(X,Y)),
inference(equational,[status(thm)],[c271,c415]) ).
cnf(c452,plain,
join(complement(composition(X,Y)),composition(join(X,Z),Y)) = top,
inference(equational,[status(thm)],[c4,c321]) ).
cnf(c460,plain,
join(complement(one),complement(composition(X,complement(converse(X))))) = top,
inference(equational,[status(thm)],[c4,c126,c145,c173]) ).
cnf(c461,plain,
meet(one,composition(X,complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c28,c29,c460]) ).
cnf(c463,plain,
meet(one,composition(converse(X),complement(X))) = zero,
inference(equational,[status(thm)],[c2,c461]) ).
cnf(c526,plain,
join(converse(join(X,Y)),complement(converse(join(Y,X)))) = top,
inference(equational,[status(thm)],[c10,c56,c62]) ).
cnf(c533,plain,
converse(join(X,join(X,Y))) = converse(join(composition(join(one,one),X),Y)),
inference(equational,[status(thm)],[c14,c20,c21,c384]) ).
cnf(c534,plain,
join(X,join(Y,X)) = join(composition(X,join(one,one)),Y),
inference(equational,[status(thm)],[c2,c10,c14,c67,c340,c533]) ).
cnf(c540,plain,
composition(top,composition(join(one,X),Y)) = composition(top,Y),
inference(equational,[status(thm)],[c51,c146,c157,c225,c443]) ).
cnf(c607,axiom,
X = join(complement(join(complement(X),complement(Y))),complement(join(complement(X),Y))),
file('REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c608,plain,
join(meet(X,Y),complement(join(complement(X),Y))) = X,
inference(equational,[status(thm)],[c28,c607]) ).
cnf(c609,plain,
join(zero,complement(complement(X))) = X,
inference(equational,[status(thm)],[c8,c141,c608]) ).
cnf(c611,plain,
join(zero,meet(one,one)) = one,
inference(equational,[status(thm)],[c143,c159,c463,c608]) ).
cnf(c612,plain,
join(zero,X) = X,
inference(equational,[status(thm)],[c153,c609]) ).
cnf(c613,plain,
complement(zero) = top,
inference(equational,[status(thm)],[c77,c144,c612]) ).
cnf(c614,plain,
join(X,zero) = X,
inference(equational,[status(thm)],[c156,c440,c612]) ).
cnf(c615,plain,
complement(complement(X)) = X,
inference(equational,[status(thm)],[c609,c612]) ).
cnf(c616,plain,
composition(X,zero) = zero,
inference(equational,[status(thm)],[c142,c359,c612]) ).
cnf(c617,plain,
meet(one,one) = one,
inference(equational,[status(thm)],[c611,c612]) ).
cnf(c618,plain,
join(X,X) = X,
inference(equational,[status(thm)],[c22,c299,c617]) ).
cnf(c620,plain,
meet(top,X) = X,
inference(equational,[status(thm)],[c33,c612,c615]) ).
cnf(c621,plain,
meet(X,top) = X,
inference(equational,[status(thm)],[c30,c620]) ).
cnf(c622,plain,
join(X,meet(X,Y)) = X,
inference(equational,[status(thm)],[c4,c22,c219,c293,c608]) ).
cnf(c623,plain,
meet(zero,X) = zero,
inference(equational,[status(thm)],[c142,c239,c612,c616,c622]) ).
cnf(c624,plain,
meet(X,zero) = zero,
inference(equational,[status(thm)],[c30,c623]) ).
cnf(c625,plain,
join(complement(X),complement(Y)) = complement(meet(X,Y)),
inference(equational,[status(thm)],[c28,c609,c612]) ).
cnf(c626,plain,
complement(meet(complement(X),Y)) = join(X,complement(Y)),
inference(equational,[status(thm)],[c33,c612,c620,c625]) ).
cnf(c627,plain,
complement(meet(X,complement(Y))) = join(complement(X),Y),
inference(equational,[status(thm)],[c33,c612,c620,c625]) ).
cnf(c628,plain,
join(X,complement(meet(X,Y))) = top,
inference(equational,[status(thm)],[c35,c145,c625]) ).
cnf(c630,plain,
complement(join(complement(X),Y)) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c33,c612,c620,c627]) ).
cnf(c631,plain,
complement(join(X,complement(Y))) = meet(complement(X),Y),
inference(equational,[status(thm)],[c609,c612,c626]) ).
cnf(c632,plain,
join(converse(zero),X) = X,
inference(equational,[status(thm)],[c2,c25,c612]) ).
cnf(c633,plain,
converse(zero) = zero,
inference(equational,[status(thm)],[c614,c632]) ).
cnf(c634,plain,
meet(X,join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c29,c608,c614,c626,c628]) ).
cnf(c635,plain,
meet(X,join(X,Y)) = X,
inference(equational,[status(thm)],[c33,c620,c634]) ).
cnf(c636,plain,
meet(X,meet(X,Y)) = meet(X,Y),
inference(equational,[status(thm)],[c30,c608,c634]) ).
cnf(c638,plain,
meet(X,join(Y,X)) = X,
inference(equational,[status(thm)],[c4,c635]) ).
cnf(c639,plain,
join(X,meet(Y,X)) = X,
inference(equational,[status(thm)],[c30,c622]) ).
cnf(c640,plain,
join(meet(X,Y),meet(X,complement(Y))) = X,
inference(equational,[status(thm)],[c4,c28,c608]) ).
cnf(c641,plain,
join(X,complement(composition(zero,X))) = top,
inference(equational,[status(thm)],[c4,c22,c452,c611]) ).
cnf(c642,plain,
composition(zero,top) = zero,
inference(equational,[status(thm)],[c146,c317,c613,c633]) ).
cnf(c646,plain,
meet(X,meet(Y,X)) = meet(X,Y),
inference(equational,[status(thm)],[c30,c636]) ).
cnf(c648,plain,
join(X,join(X,complement(Y))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c14,c141,c178,c626]) ).
cnf(c649,plain,
join(X,join(X,Y)) = join(X,Y),
inference(equational,[status(thm)],[c33,c612,c615,c620,c648]) ).
cnf(c650,plain,
join(X,join(Y,X)) = join(X,Y),
inference(equational,[status(thm)],[c1,c534,c618,c649]) ).
cnf(c652,plain,
join(meet(X,Y),meet(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c30,c640]) ).
cnf(c653,plain,
composition(converse(sk1),complement(sk1)) = zero,
inference(equational,[status(thm)],[c29,c142,c237,c624,c652]) ).
cnf(c654,plain,
join(meet(X,Y),meet(complement(Y),X)) = X,
inference(equational,[status(thm)],[c30,c640]) ).
cnf(c657,plain,
composition(zero,X) = zero,
inference(equational,[status(thm)],[c146,c271,c614,c642]) ).
cnf(c658,plain,
complement(composition(converse(complement(sk1)),sk1)) = top,
inference(equational,[status(thm)],[c31,c378,c612,c633,c648]) ).
cnf(c659,plain,
composition(complement(sk1),top) = complement(sk1),
inference(equational,[status(thm)],[c97,c146,c232,c658]) ).
cnf(c663,plain,
join(meet(X,Y),meet(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c30,c654]) ).
cnf(c667,plain,
meet(meet(X,Y),complement(meet(Y,X))) = zero,
inference(equational,[status(thm)],[c136,c625]) ).
cnf(c670,plain,
join(complement(X),join(complement(Y),Z)) = join(complement(meet(X,Y)),Z),
inference(equational,[status(thm)],[c14,c625]) ).
cnf(c671,plain,
complement(meet(meet(X,Y),Z)) = complement(meet(X,meet(Y,Z))),
inference(equational,[status(thm)],[c625,c670]) ).
cnf(c672,plain,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(equational,[status(thm)],[c609,c612,c615,c671]) ).
cnf(c673,plain,
meet(X,meet(Y,Z)) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c30,c672]) ).
cnf(c674,plain,
join(complement(X),join(Y,complement(Z))) = join(Y,complement(meet(X,Z))),
inference(equational,[status(thm)],[c26,c625]) ).
cnf(c676,plain,
meet(X,meet(Y,complement(meet(X,Y)))) = zero,
inference(equational,[status(thm)],[c30,c83,c612,c615,c621,c625,c667,c673]) ).
cnf(c697,plain,
join(X,complement(meet(Y,join(X,complement(Y))))) = top,
inference(equational,[status(thm)],[c54,c625]) ).
cnf(c706,plain,
join(meet(complement(X),Y),complement(Z)) = complement(meet(join(X,complement(Y)),Z)),
inference(equational,[status(thm)],[c626]) ).
cnf(c714,plain,
join(converse(X),complement(converse(meet(complement(Y),X)))) = top,
inference(equational,[status(thm)],[c4,c125,c147,c654]) ).
cnf(c717,plain,
join(X,join(Y,meet(X,Z))) = join(Y,X),
inference(equational,[status(thm)],[c26,c622]) ).
cnf(c718,plain,
join(complement(X),meet(X,Y)) = join(complement(X),Y),
inference(equational,[status(thm)],[c4,c663,c717]) ).
cnf(c722,plain,
join(X,join(meet(X,Y),Z)) = join(X,Z),
inference(equational,[status(thm)],[c14,c622]) ).
cnf(c726,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(equational,[status(thm)],[c29,c41,c148,c608,c614]) ).
cnf(c729,plain,
complement(meet(converse(X),converse(complement(X)))) = top,
inference(equational,[status(thm)],[c2,c615,c625,c714,c726]) ).
cnf(c730,plain,
meet(converse(X),converse(complement(X))) = zero,
inference(equational,[status(thm)],[c621,c676,c729]) ).
cnf(c732,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(equational,[status(thm)],[c2,c730]) ).
cnf(c733,plain,
converse(complement(converse(complement(X)))) = X,
inference(equational,[status(thm)],[c614,c663,c726,c732]) ).
cnf(c734,plain,
complement(converse(complement(X))) = converse(X),
inference(equational,[status(thm)],[c2,c733]) ).
cnf(c735,plain,
complement(converse(X)) = converse(complement(X)),
inference(equational,[status(thm)],[c615,c734]) ).
cnf(c779,plain,
meet(complement(X),meet(Y,join(complement(Y),X))) = zero,
inference(equational,[status(thm)],[c627,c667,c672]) ).
cnf(c784,plain,
meet(complement(meet(X,Y)),join(complement(X),Y)) = complement(X),
inference(equational,[status(thm)],[c61,c608,c625]) ).
cnf(c785,plain,
meet(join(X,Y),join(X,complement(Y))) = X,
inference(equational,[status(thm)],[c30,c33,c612,c615,c620,c626,c784]) ).
cnf(c786,plain,
join(X,meet(Y,join(X,complement(Y)))) = X,
inference(equational,[status(thm)],[c621,c697,c785]) ).
cnf(c787,plain,
meet(join(X,Y),join(complement(Y),X)) = X,
inference(equational,[status(thm)],[c4,c785]) ).
cnf(c788,plain,
meet(X,join(complement(X),Y)) = meet(X,Y),
inference(equational,[status(thm)],[c14,c627,c639,c640,c787]) ).
cnf(c789,plain,
meet(X,join(Y,complement(X))) = meet(X,Y),
inference(equational,[status(thm)],[c14,c626,c650,c654,c718,c787]) ).
cnf(c790,plain,
meet(X,complement(meet(Y,X))) = meet(X,complement(Y)),
inference(equational,[status(thm)],[c625,c789]) ).
cnf(c791,plain,
join(X,complement(join(Y,X))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c615,c626,c789]) ).
cnf(c792,plain,
meet(complement(X),join(Y,X)) = meet(complement(X),Y),
inference(equational,[status(thm)],[c33,c612,c620,c789]) ).
cnf(c794,plain,
meet(complement(X),join(X,Y)) = meet(complement(X),Y),
inference(equational,[status(thm)],[c33,c612,c620,c788]) ).
cnf(c795,plain,
meet(join(X,Y),join(Y,complement(X))) = Y,
inference(equational,[status(thm)],[c4,c785]) ).
cnf(c796,plain,
join(converse(X),complement(one)) = converse(join(X,complement(one))),
inference(equational,[status(thm)],[c10,c39,c735,c791]) ).
cnf(c798,plain,
meet(join(X,Y),join(complement(X),Y)) = Y,
inference(equational,[status(thm)],[c4,c787]) ).
cnf(c800,plain,
join(complement(X),meet(Y,X)) = join(complement(X),Y),
inference(equational,[status(thm)],[c627,c790]) ).
cnf(c803,plain,
join(complement(one),converse(X)) = converse(join(X,complement(one))),
inference(equational,[status(thm)],[c4,c796]) ).
cnf(c804,plain,
converse(meet(one,complement(X))) = meet(one,converse(complement(X))),
inference(equational,[status(thm)],[c30,c631,c735,c796]) ).
cnf(c805,plain,
converse(meet(one,X)) = meet(one,converse(X)),
inference(equational,[status(thm)],[c615,c804]) ).
cnf(c806,plain,
converse(meet(X,one)) = meet(one,converse(X)),
inference(equational,[status(thm)],[c30,c805]) ).
cnf(c833,plain,
meet(X,meet(join(Y,X),Z)) = meet(X,Z),
inference(equational,[status(thm)],[c638,c672]) ).
cnf(c836,plain,
meet(X,meet(Y,join(Z,X))) = meet(Y,X),
inference(equational,[status(thm)],[c638,c673]) ).
cnf(c844,plain,
join(meet(X,Y),join(Z,meet(X,complement(Y)))) = join(Z,X),
inference(equational,[status(thm)],[c26,c640]) ).
cnf(c850,plain,
complement(composition(join(one,X),complement(Y))) = meet(Y,complement(composition(X,complement(Y)))),
inference(equational,[status(thm)],[c51,c630]) ).
cnf(c866,plain,
join(X,join(Y,complement(meet(join(X,Y),Z)))) = top,
inference(equational,[status(thm)],[c435,c625]) ).
cnf(c871,plain,
join(X,join(Y,complement(join(X,meet(Y,Z))))) = top,
inference(equational,[status(thm)],[c4,c435,c844]) ).
cnf(c878,plain,
meet(X,complement(composition(top,complement(X)))) = complement(composition(top,complement(X))),
inference(equational,[status(thm)],[c613,c641,c657,c850]) ).
cnf(c883,plain,
join(sk1,complement(meet(composition(sk1,X),Y))) = top,
inference(equational,[status(thm)],[c2,c382,c620,c625,c735,c866]) ).
cnf(c894,plain,
join(X,meet(Y,complement(meet(X,Z)))) = join(X,Y),
inference(equational,[status(thm)],[c60,c621,c625,c717,c798,c871]) ).
cnf(c897,plain,
composition(join(converse(complement(sk1)),X),sk1) = composition(X,sk1),
inference(equational,[status(thm)],[c2,c12,c93,c247,c612,c653]) ).
cnf(c898,plain,
composition(converse(sk1),sk1) = composition(top,sk1),
inference(equational,[status(thm)],[c6,c734,c897]) ).
cnf(c899,plain,
converse(composition(top,sk1)) = composition(top,sk1),
inference(equational,[status(thm)],[c19,c898]) ).
cnf(c908,plain,
meet(X,meet(Y,meet(Z,X))) = meet(Y,meet(X,Z)),
inference(equational,[status(thm)],[c646,c673]) ).
cnf(c916,plain,
join(complement(one),join(X,composition(converse(Y),complement(Y)))) = join(X,complement(one)),
inference(equational,[status(thm)],[c26,c159]) ).
cnf(c919,plain,
join(meet(X,Y),join(meet(complement(Y),X),Z)) = join(X,Z),
inference(equational,[status(thm)],[c14,c654]) ).
cnf(c920,plain,
join(X,join(meet(complement(X),Y),Z)) = join(X,join(Y,Z)),
inference(equational,[status(thm)],[c14,c631,c638,c672,c785,c919]) ).
cnf(c935,plain,
meet(join(X,Y),meet(Z,Y)) = meet(Y,Z),
inference(equational,[status(thm)],[c833,c836,c908]) ).
cnf(c936,plain,
join(meet(X,complement(Y)),join(Z,meet(X,Y))) = join(Z,X),
inference(equational,[status(thm)],[c33,c612,c620,c844]) ).
cnf(c938,plain,
join(X,meet(join(complement(X),Y),Z)) = join(Z,X),
inference(equational,[status(thm)],[c4,c627,c920,c936]) ).
cnf(c965,plain,
join(meet(X,Y),join(Z,meet(Y,complement(X)))) = join(Z,Y),
inference(equational,[status(thm)],[c26,c652]) ).
cnf(c966,plain,
join(complement(X),join(Y,meet(Z,X))) = join(Y,join(complement(X),Z)),
inference(equational,[status(thm)],[c615,c784,c935,c965]) ).
cnf(c969,plain,
join(complement(X),join(Y,meet(X,Z))) = join(Y,join(complement(X),Z)),
inference(equational,[status(thm)],[c30,c966]) ).
cnf(c970,plain,
join(meet(X,complement(Y)),join(Z,X)) = join(X,Z),
inference(equational,[status(thm)],[c630,c722,c938,c969]) ).
cnf(c971,plain,
join(meet(X,Y),join(Z,X)) = join(X,Z),
inference(equational,[status(thm)],[c33,c620,c970]) ).
cnf(c972,plain,
join(meet(X,Y),join(Z,Y)) = join(Y,Z),
inference(equational,[status(thm)],[c30,c971]) ).
cnf(c996,plain,
converse(join(complement(X),composition(complement(composition(X,Y)),converse(Y)))) = converse(complement(X)),
inference(equational,[status(thm)],[c2,c12,c89,c140,c735]) ).
cnf(c997,plain,
join(complement(X),composition(complement(composition(X,Y)),converse(Y))) = complement(X),
inference(equational,[status(thm)],[c2,c996]) ).
cnf(c1000,plain,
join(X,composition(complement(composition(complement(X),Y)),converse(Y))) = X,
inference(equational,[status(thm)],[c33,c612,c615,c620,c997]) ).
cnf(c1015,plain,
join(X,complement(join(Y,meet(X,Z)))) = join(X,complement(Y)),
inference(equational,[status(thm)],[c620,c635,c674,c798,c871]) ).
cnf(c1016,plain,
join(X,meet(complement(Y),join(X,meet(Y,Z)))) = X,
inference(equational,[status(thm)],[c620,c631,c785,c871]) ).
cnf(c1017,plain,
meet(complement(X),join(Y,meet(X,Z))) = meet(Y,complement(X)),
inference(equational,[status(thm)],[c631,c646,c706,c790,c795,c1015,c1016]) ).
cnf(c1019,plain,
meet(X,join(Y,meet(complement(X),Z))) = meet(Y,X),
inference(equational,[status(thm)],[c33,c612,c615,c620,c1017]) ).
cnf(c1082,plain,
join(composition(X,Y),complement(composition(meet(Z,X),Y))) = top,
inference(equational,[status(thm)],[c4,c452,c652]) ).
cnf(c1083,plain,
join(X,complement(composition(meet(Y,one),X))) = top,
inference(equational,[status(thm)],[c22,c1082]) ).
cnf(c1086,plain,
join(sk1,complement(composition(meet(X,sk1),top))) = top,
inference(equational,[status(thm)],[c3,c1082]) ).
cnf(c1090,plain,
meet(X,composition(meet(Y,one),complement(X))) = zero,
inference(equational,[status(thm)],[c30,c615,c621,c779,c1083]) ).
cnf(c1099,plain,
meet(X,composition(meet(one,Y),complement(X))) = zero,
inference(equational,[status(thm)],[c30,c1090]) ).
cnf(c1108,plain,
join(complement(composition(X,Y)),composition(X,join(Z,Y))) = top,
inference(equational,[status(thm)],[c126,c147,c271]) ).
cnf(c1109,plain,
join(composition(X,top),complement(composition(X,Y))) = top,
inference(equational,[status(thm)],[c4,c109,c146,c621,c1108]) ).
cnf(c1110,plain,
meet(composition(X,Y),composition(X,top)) = composition(X,Y),
inference(equational,[status(thm)],[c621,c789,c1109]) ).
cnf(c1118,plain,
meet(complement(sk1),composition(complement(sk1),X)) = composition(complement(sk1),X),
inference(equational,[status(thm)],[c30,c659,c1110]) ).
cnf(c1127,plain,
composition(converse(join(complement(sk1),X)),sk1) = composition(converse(X),sk1),
inference(equational,[status(thm)],[c19,c270,c612,c653]) ).
cnf(c1128,plain,
composition(converse(meet(X,sk1)),sk1) = composition(converse(X),sk1),
inference(equational,[status(thm)],[c800,c1127]) ).
cnf(c1146,plain,
complement(meet(composition(X,Y),composition(join(Z,X),Y))) = complement(composition(X,Y)),
inference(equational,[status(thm)],[c321,c621,c784]) ).
cnf(c1147,plain,
meet(composition(X,Y),composition(join(Z,X),Y)) = composition(X,Y),
inference(equational,[status(thm)],[c609,c612,c615,c1146]) ).
cnf(c1225,plain,
converse(join(X,join(Y,join(converse(Z),W)))) = join(Z,converse(join(X,join(Y,W)))),
inference(equational,[status(thm)],[c14,c66]) ).
cnf(c1226,plain,
join(converse(X),join(Y,complement(one))) = join(Y,converse(join(X,complement(one)))),
inference(equational,[status(thm)],[c25,c159,c796,c916,c1225]) ).
cnf(c1228,plain,
join(converse(X),join(complement(one),Y)) = join(Y,converse(join(X,complement(one)))),
inference(equational,[status(thm)],[c4,c1226]) ).
cnf(c1229,plain,
join(converse(join(X,complement(one))),Y) = join(converse(X),join(Y,complement(one))),
inference(equational,[status(thm)],[c4,c1226]) ).
cnf(c1231,plain,
join(X,converse(join(complement(one),Y))) = join(converse(Y),join(complement(one),X)),
inference(equational,[status(thm)],[c4,c1228]) ).
cnf(c1260,plain,
composition(top,composition(converse(composition(X,sk1)),Y)) = composition(converse(composition(X,sk1)),Y),
inference(equational,[status(thm)],[c58,c290]) ).
cnf(c1261,plain,
composition(converse(sk1),composition(top,X)) = composition(top,composition(sk1,X)),
inference(equational,[status(thm)],[c16,c290,c434,c899,c1260]) ).
cnf(c1336,plain,
join(composition(X,Y),join(Z,composition(X,W))) = join(Z,composition(X,join(Y,W))),
inference(equational,[status(thm)],[c26,c271]) ).
cnf(c1357,plain,
meet(converse(join(X,Y)),converse(join(X,complement(Y)))) = converse(X),
inference(equational,[status(thm)],[c10,c735,c785]) ).
cnf(c1358,plain,
meet(converse(X),converse(join(Y,complement(X)))) = converse(meet(X,Y)),
inference(equational,[status(thm)],[c30,c608,c972,c1357]) ).
cnf(c1359,plain,
converse(meet(converse(X),Y)) = meet(X,converse(Y)),
inference(equational,[status(thm)],[c2,c25,c735,c789,c1358]) ).
cnf(c1360,plain,
converse(meet(X,converse(Y))) = meet(converse(X),Y),
inference(equational,[status(thm)],[c2,c1359]) ).
cnf(c1365,plain,
meet(converse(X),join(Y,converse(complement(X)))) = meet(converse(X),Y),
inference(equational,[status(thm)],[c24,c1358,c1360]) ).
cnf(c1415,plain,
meet(X,join(Y,complement(composition(top,X)))) = meet(Y,X),
inference(equational,[status(thm)],[c615,c878,c1019]) ).
cnf(c1430,plain,
join(X,meet(Y,composition(top,complement(X)))) = join(X,Y),
inference(equational,[status(thm)],[c615,c878,c894]) ).
cnf(c1435,plain,
join(complement(one),join(X,composition(Y,converse(complement(Y))))) = join(X,complement(one)),
inference(equational,[status(thm)],[c2,c735,c916]) ).
cnf(c1522,plain,
meet(composition(X,Y),composition(meet(Z,X),Y)) = composition(meet(Z,X),Y),
inference(equational,[status(thm)],[c30,c786,c789,c1147]) ).
cnf(c1523,plain,
join(sk1,complement(composition(meet(X,sk1),Y))) = top,
inference(equational,[status(thm)],[c883,c1522]) ).
cnf(c1539,plain,
join(converse(join(X,join(one,Y))),Z) = join(one,join(Z,converse(join(Y,X)))),
inference(equational,[status(thm)],[c1,c104,c226]) ).
cnf(c1542,plain,
join(X,composition(Y,join(X,Z))) = join(composition(join(one,Y),X),composition(Y,Z)),
inference(equational,[status(thm)],[c212,c271]) ).
cnf(c1544,plain,
join(X,composition(Y,join(X,Z))) = join(composition(join(Y,one),X),composition(Y,Z)),
inference(equational,[status(thm)],[c213,c271]) ).
cnf(c1565,plain,
composition(converse(X),join(Y,complement(composition(X,top)))) = composition(converse(X),Y),
inference(equational,[status(thm)],[c189,c612,c614,c1336]) ).
cnf(c1567,plain,
converse(composition(top,meet(X,sk1))) = composition(converse(X),sk1),
inference(equational,[status(thm)],[c166,c1086,c1128,c1565]) ).
cnf(c1568,plain,
composition(top,meet(X,sk1)) = composition(converse(sk1),X),
inference(equational,[status(thm)],[c2,c19,c1567]) ).
cnf(c1569,plain,
composition(top,meet(sk1,X)) = composition(converse(sk1),X),
inference(equational,[status(thm)],[c30,c1568]) ).
cnf(c1656,plain,
join(X,converse(join(complement(one),Y))) = join(complement(one),join(X,converse(Y))),
inference(equational,[status(thm)],[c4,c14,c1231]) ).
cnf(c1683,plain,
composition(converse(meet(X,Y)),composition(Y,top)) = converse(composition(top,meet(X,Y))),
inference(equational,[status(thm)],[c166,c1082,c1565]) ).
cnf(c1684,plain,
composition(meet(one,converse(X)),top) = converse(composition(top,meet(X,one))),
inference(equational,[status(thm)],[c20,c21,c806,c1683]) ).
cnf(c1721,plain,
meet(sk1,composition(meet(X,sk1),Y)) = composition(meet(X,sk1),Y),
inference(equational,[status(thm)],[c30,c615,c621,c792,c1523]) ).
cnf(c1722,plain,
composition(meet(one,sk1),complement(sk1)) = zero,
inference(equational,[status(thm)],[c1099,c1721]) ).
cnf(c1746,plain,
join(composition(top,X),composition(converse(sk1),Y)) = composition(top,join(X,composition(converse(sk1),Y))),
inference(equational,[status(thm)],[c147,c290,c443,c1544]) ).
cnf(c1747,plain,
composition(converse(join(one,sk1)),composition(top,X)) = composition(top,X),
inference(equational,[status(thm)],[c39,c51,c225,c540,c1261,c1746]) ).
cnf(c1754,plain,
meet(X,complement(composition(complement(composition(X,Y)),converse(Y)))) = X,
inference(equational,[status(thm)],[c615,c630,c1000]) ).
cnf(c1757,plain,
meet(one,meet(sk1,converse(sk1))) = meet(one,sk1),
inference(equational,[status(thm)],[c167,c613,c659,c672,c734,c1722,c1754]) ).
cnf(c1928,plain,
join(composition(X,Y),composition(Z,join(W,Y))) = join(composition(join(Z,X),Y),composition(Z,W)),
inference(equational,[status(thm)],[c271,c400]) ).
cnf(c1929,plain,
join(sk1,composition(join(sk1,X),Y)) = join(sk1,composition(X,Y)),
inference(equational,[status(thm)],[c4,c169,c280,c1539,c1928]) ).
cnf(c1930,plain,
join(sk1,composition(complement(sk1),X)) = join(sk1,composition(top,X)),
inference(equational,[status(thm)],[c6,c1929]) ).
cnf(c1931,plain,
meet(complement(sk1),composition(top,X)) = composition(complement(sk1),X),
inference(equational,[status(thm)],[c794,c1118,c1930]) ).
cnf(c1935,plain,
join(sk1,complement(composition(top,X))) = complement(composition(complement(sk1),X)),
inference(equational,[status(thm)],[c626,c1931]) ).
cnf(c1939,plain,
join(sk1,converse(join(sk1,complement(one)))) = join(sk1,complement(one)),
inference(equational,[status(thm)],[c3,c4,c167,c615,c1435,c1656,c1930]) ).
cnf(c1940,plain,
join(sk1,converse(complement(meet(one,sk1)))) = top,
inference(equational,[status(thm)],[c14,c24,c30,c526,c625,c631,c718,c735,c803,c806,c1229,c1939]) ).
cnf(c1942,plain,
meet(one,converse(sk1)) = meet(one,sk1),
inference(equational,[status(thm)],[c30,c621,c672,c805,c1365,c1757,c1940]) ).
cnf(c1944,plain,
composition(meet(one,sk1),top) = sk1,
inference(equational,[status(thm)],[c1,c2,c1569,c1684,c1942]) ).
cnf(c1951,plain,
join(X,composition(complement(sk1),complement(X))) = join(X,complement(sk1)),
inference(equational,[status(thm)],[c1430,c1931]) ).
cnf(c1968,plain,
meet(X,complement(composition(complement(sk1),X))) = meet(X,sk1),
inference(equational,[status(thm)],[c615,c625,c630,c1951]) ).
cnf(c2281,plain,
composition(join(one,sk1),complement(composition(top,X))) = complement(composition(top,X)),
inference(equational,[status(thm)],[c2,c51,c140,c649,c1747]) ).
cnf(c2424,plain,
join(X,composition(Y,join(Z,X))) = join(composition(join(one,Y),X),composition(Y,Z)),
inference(equational,[status(thm)],[c4,c1542]) ).
cnf(c2425,plain,
join(composition(sk1,X),complement(composition(top,X))) = complement(composition(complement(sk1),X)),
inference(equational,[status(thm)],[c4,c353,c1935,c2281,c2424]) ).
cnf(c2426,plain,
meet(X,composition(sk1,X)) = meet(X,sk1),
inference(equational,[status(thm)],[c30,c1415,c1968,c2425]) ).
cnf(c2561,plain,
join(X,composition(meet(Y,one),join(X,Z))) = join(X,composition(meet(Y,one),Z)),
inference(equational,[status(thm)],[c22,c786,c789,c1542]) ).
cnf(c2564,plain,
join(X,composition(meet(Y,one),complement(X))) = join(X,composition(meet(Y,one),top)),
inference(equational,[status(thm)],[c6,c2561]) ).
cnf(c2565,plain,
meet(X,composition(meet(Y,one),top)) = composition(meet(Y,one),X),
inference(equational,[status(thm)],[c22,c51,c615,c639,c788,c798,c2564]) ).
cnf(c2567,plain,
meet(X,composition(meet(one,Y),top)) = composition(meet(Y,one),X),
inference(equational,[status(thm)],[c30,c2565]) ).
cnf(c2568,plain,
composition(meet(one,sk1),X) = meet(X,sk1),
inference(equational,[status(thm)],[c1,c30,c1944,c2426,c2567]) ).
cnf(c2570,plain,
composition(meet(X,sk1),Y) = meet(sk1,composition(X,Y)),
inference(equational,[status(thm)],[c16,c30,c2568]) ).
cnf(g1,plain,
composition(meet(sk1,sk2),sk3) = meet(sk1,composition(sk2,sk3)),
inference(equational,[status(thm)],[c30,c2570]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL033-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 16:14:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 234.84/235.25 % SZS status Unsatisfiable
% 234.84/235.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------